Answer
$\lim\limits_{x \to -2} (3x+5)= -1$
Work Step by Step
Let $\epsilon \gt 0$ be given.
Let $\delta = \frac{\epsilon}{3}$
Suppose that $\vert x-(-2) \vert \lt \delta$.
Note that $~~\vert x-(-2) \vert = \vert x+2 \vert$
Then:
$\vert (3x+5)-(-1) \vert = \vert 3x+6 \vert = \vert 3(x+2) \vert = 3\vert x+2 \vert \lt 3\delta = 3(\frac{\epsilon}{3}) = \epsilon$
Therefore, $\lim\limits_{x \to -2} (3x+5)= -1$
